Chapter 12: Problem 1
Suppose all firms in a monopolistically competitive industry were merged into one large firm. Would that new firm produce as many different brands? Would it produce only a single brand? Explain.
Chapter 12: Problem 1
Suppose all firms in a monopolistically competitive industry were merged into one large firm. Would that new firm produce as many different brands? Would it produce only a single brand? Explain.
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Get started for freeSuppose that two identical firms produce widgets and that they are the only firms in the market. Their costs are given by \(C_{1}=60 Q_{1}\) and \(C_{2}=60 Q_{2}\), where \(Q_{1}\) is the output of Firm 1 and \(Q_{2}\) the output of Firm 2. Price is determined by the following demand curve: $$P=300-Q$$ where \(Q=Q_{1}+Q_{2}\) a. Find the Cournot-Nash equilibrium. Calculate the profit of each firm at this equilibrium. b. Suppose the two firms form a cartel to maximize joint profits. How many widgets will be produced? Calculate each firm's profit. c. Suppose Firm 1 were the only firm in the industry. How would market output and Firm \(1^{\prime}\) s profit differ from that found in part (b) above? d. Returning to the duopoly of part (b), suppose Firm 1 abides by the agreement but Firm 2 cheats by increasing production. How many widgets will Firm 2 produce? What will be each firm's profits?
Consider two firms facing the demand curve \(P=50-5 Q,\) where \(Q=Q_{1}+Q_{2}\). The firms' cost functions are \(C_{1}\left(Q_{1}\right)=20+10 Q_{1}\) and \(C_{2}\left(Q_{2}\right)=10+12 Q_{2}\) a. Suppose both firms have entered the industry. What is the joint profit- maximizing level of output? How much will each firm produce? How would your answer change if the firms have not yet entered the industry? b. What is each firm's equilibrium output and profit if they behave noncooperatively? Use the Cournot model. Draw the firms' reaction curves and show the equilibrium. c. How much should Firm 1 be willing to pay to purchase Firm 2 if collusion is illegal but a takeover is not?
Two firms produce luxury sheepskin auto seat covers: Western Where (WW) and B.B.B. Sheep (BBBS). Each firm has a cost function given by $$C(q)=30 q+1.5 q^{2}$$ The market demand for these seat covers is represented by the inverse demand equation $$P=300-3 Q$$ where \(Q=q_{1}+q_{2},\) total output. a. If each firm acts to maximize its profits, taking its rival's output as given (i.e., the firms behave as Cournot oligopolists), what will be the equilibrium quantities selected by each firm? What is total output, and what is the market price? What are the profits for each firm? b. It occurs to the managers of \(\mathrm{WW}\) and \(\mathrm{BBBS}\) that they could do a lot better by colluding. If the two firms collude, what will be the profit-maximizing choice of output? The industry price? The output and the profit for each firm in this case? c. The managers of these firms realize that explicit agreements to collude are illegal. Each firm must decide on its own whether to produce the Cournot quantity or the cartel quantity. To aid in making the decision, the manager of WW constructs a payoff matrix like the one below. Fill in each box with the profit of \(\mathrm{WW}\) and the profit of BBBS. Given this payoff matrix, what output strategy is each firm likely to pursue? d. Suppose WW can set its output level before BBBS does. How much will WW choose to produce in this case? How much will BBBS produce? What is the market price, and what is the profit for each firm? Is WW better off by choosing its output first? Explain why or why not.
A monopolist can produce at a constant average (and marginal) cost of \(\mathrm{AC}=\mathrm{MC}=\$ 5 .\) It faces a market demand curve given by \(Q=53-P\) a. Calculate the profit-maximizing price and quantity for this monopolist. Also calculate its profits. b. Suppose a second firm enters the market. Let \(Q_{1}\) be the output of the first firm and \(Q_{2}\) be the output of the second. Market demand is now given by $$Q_{1}+Q_{2}=53-P$$ Assuming that this second firm has the same costs as the first, write the profits of each firm as functions of \(Q_{1}\) and \(Q_{2}\) c. Suppose (as in the Cournot model) that each firm chooses its profit- maximizing level of output on the assumption that its competitor's output is fixed. Find each firm's "reaction curve" (i.e., the rule that gives its desired output in terms of its competitor's output). d. Calculate the Cournot equilibrium (i.e., the values of \(Q_{1}\) and \(Q_{2}\) for which each firm is doing as well as it can given its competitor's output). What are the resulting market price and profits of each firm? *e. Suppose there are \(N\) firms in the industry, all with the same constant marginal cost, \(\mathrm{MC}=\$ 5 .\) Find the Cournot equilibrium. How much will each firm produce, what will be the market price, and how much profit will each firm earn? Also, show that as \(N\) becomes large, the market price approaches the price that would prevail under perfect competition.
Two firms compete in selling identical widgets. They choose their output levels \(Q_{1}\) and \(Q_{2}\) simultaneously and face the demand curve $$P=30-Q$$ where \(Q=Q_{1}+Q_{2}\). Until recently, both firms had zero marginal costs. Recent environmental regulations have increased Firm \(2^{\prime}\) s marginal cost to \(\$ 15 .\) Firm \(1^{\prime}\) s marginal cost remains constant at zero. True or false: As a result, the market price will rise to the monopoly level Suppose that two identical firms produce widgets and
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